Morphological Plant Modeling

17 Pages·2017·7.8 MB·English

Morphological Plant Modeling: Unleashing Geometric
and Topological Potential within the Plant Sciences
Alexander B Bucksch, Acheampong Atta-Boateng, Akomian F Azihou,
Dorjsuren P Battogtokh, Aly B Baumgartner, Brad N Binder, Siobhan A
Braybrook, Cynthia Chang, Viktoirya C Coneva, Thomas P Dewitt, et al.
To cite this version:
AlexanderBBucksch,AcheampongAtta-Boateng,AkomianFAzihou,DorjsurenPBattogtokh,AlyB
Baumgartner, et al.. Morphological Plant Modeling: Unleashing Geometric and Topological Potential
within the Plant Sciences. Frontiers in Plant Science, 2017, 8 (900), pp.16. ￿10.3389/fpls.2017.00900￿.
￿hal-01537909￿
HAL Id: hal-01537909
https://hal.inria.fr/hal-01537909
Submitted on 13 Jun 2017
HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est
archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents
entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non,
lished or not. The documents may come from émanant des établissements d’enseignement et de
teaching and research institutions in France or recherche français ou étrangers, des laboratoires
abroad, or from public or private research centers. publics ou privés.
fpls-08-00900 June8,2017 Time:16:13 #1
REVIEW
published:09June2017
doi:10.3389/fpls.2017.00900
Morphological Plant Modeling:
Unleashing Geometric and
Topological Potential within the Plant
Sciences
AlexanderBucksch1,2,3*,AcheampongAtta-Boateng4,AkomianF.Azihou5,
DorjsurenBattogtokh6,AlyBaumgartner7,BradM.Binder8,SiobhanA.Braybrook9,
Editedby:
CynthiaChang10,ViktoiryaConeva11,ThomasJ.DeWitt12,AlexanderG.Fletcher13,
KatrinKahlen,
MaliaA.Gehan11,DiegoHernanDiaz-Martinez14,LilanHong15,AnjaliS.Iyer-Pascuzzi16,
HochschuleGeisenheimUniversity,
LauraL.Klein17,SamuelLeiboff18,MaoLi14,JonathanP.Lynch19,AlexisMaizel20,
Germany
JulinN.Maloof21,R.J.CodyMarkelz21,CieraC.Martinez22,LauraA.Miller23,
Reviewedby:
WashingtonMio14,WojtekPalubicki9,HendrikPoorter24,ChristophePradal25,
EvelyneCostes,
CharlesA.Price26,EetuPuttonen27,28,JohnB.Reese29,RubénRellán-Álvarez30,
InstitutNationaldelaRecherche
EdgarP.Spalding31,ErinE.Sparks32,ChristopherN.Topp11,JosephH.Williams29and
Agronomique(INRA),France
DanielH.Chitwood11*
LeoMarcelis,
WageningenUniversityandResearch,
1DepartmentofPlantBiology,UniversityofGeorgia,Athens,GA,UnitedStates,2WarnellSchoolofForestryandNatural
Netherlands
Resources,UniversityofGeorgia,Athens,GA,UnitedStates,3InstituteofBioinformatics,UniversityofGeorgia,Athens,GA,
*Correspondence: UnitedStates,4SchoolofForestryandEnvironmentalStudies,YaleUniversity,NewHaven,CT,UnitedStates,5Laboratory
AlexanderBucksch ofAppliedEcology,FacultyofAgronomicSciences,UniversityofAbomey-Calavi,Cotonou,Benin,6DepartmentofBiological
[email protected] Sciences,VirginiaPolytechnicInstituteandStateUniversity,Blacksburg,VA,UnitedStates,7DepartmentofGeosciences,
DanielH.Chitwood BaylorUniversity,Waco,TX,UnitedStates,8DepartmentofBiochemistryandCellularandMolecularBiology,Universityof
[email protected] Tennessee,Knoxville,Knoxville,TN,UnitedStates,9TheSainsburyLaboratory,UniversityofCambridge,Cambridge,United
Kingdom,10DivisionofBiology,UniversityofWashington,Bothell,WA,UnitedStates,11DonaldDanforthPlantScience
Specialtysection: Center,St.Louis,MO,UnitedStates,12DepartmentofWildlifeandFisheriesSciences–DepartmentofPlantPathologyand
Thisarticlewassubmittedto Microbiology,TexasA&MUniversity,CollegeStation,TX,UnitedStates,13SchoolofMathematicsandStatisticsandBateson
PlantBiophysicsandModeling, Centre,UniversityofSheffield,Sheffield,UnitedKingdom,14DepartmentofMathematics,FloridaStateUniversity,
asectionofthejournal Tallahassee,FL,UnitedStates,15WeillInstituteforCellandMolecularBiologyandSectionofPlantBiology,Schoolof
FrontiersinPlantScience IntegrativePlantSciences,CornellUniversity,Ithaca,NY,UnitedStates,16DepartmentofBotanyandPlantPathology,
PurdueUniversity,WestLafayette,IN,UnitedStates,17DepartmentofBiology,SaintLouisUniversity,St.Louis,MO,United
Received:05October2016
States,18SchoolofIntegrativePlantScience,CornellUniversity,Ithaca,NY,UnitedStates,19DepartmentofPlantScience,
Accepted:12May2017
ThePennsylvaniaStateUniversity,UniversityPark,PA,UnitedStates,20CenterforOrganismalStudies,Heidelberg
Published:09June2017
University,Heidelberg,Germany,21DepartmentofPlantBiology,UniversityofCalifornia,Davis,Davis,CA,UnitedStates,
Citation: 22DepartmentofMolecularandCellBiology,UniversityofCalifornia,Berkeley,Berkeley,CA,UnitedStates,23Programin
Bucksch A,Atta-Boateng A, BioinformaticsandComputationalBiology,TheUniversityofNorthCarolina,ChapelHill,NC,UnitedStates,24PlantSciences
Azihou AF,Battogtokh D, (IBG-2),ForschungszentrumJülichGmbH,Jülich,Germany,25CIRAD,UMRAGAP,INRIA,VirtualPlants,Montpellier,France,
Baumgartner A,Binder BM, 26NationalInstituteforMathematicalandBiologicalSynthesis,UniversityofTennessee,Knoxville,Knoxville,TN,United
Braybrook SA,Chang C,Coneva V, States,27DepartmentofRemoteSensingandPhotogrammetry,FinnishGeospatialResearchInstitute,NationalLandSurvey
DeWitt TJ,Fletcher AG,Gehan MA, ofFinland,Masala,Finland,28CentreofExcellenceinLaserScanningResearch,NationalLandSurveyofFinland,Masala,
Diaz-Martinez DH,Hong L, Finland,29DepartmentofEcologyandEvolutionaryBiology,UniversityofTennessee,Knoxville,Knoxville,TN,UnitedStates,
Iyer-Pascuzzi AS,Klein LL,Leiboff S, 30UnidaddeGenómicaAvanzada,LaboratorioNacionaldeGenómicaparalaBiodiversidad,CenterforResearchand
Li M,Lynch JP,Maizel A,Maloof JN, AdvancedStudiesoftheNationalPolytechnicInstitute(CINVESTAV),Irapuato,Mexico,31DepartmentofBotany,University
Markelz RJC,Martinez CC,Miller LA, ofWisconsin–Madison,Madison,WI,UnitedStates,32DepartmentofPlantandSoilSciencesandDelawareBiotechnology
Mio W,Palubicki W,Poorter H, Institute,UniversityofDelaware,Newark,DE,UnitedStates
Pradal C,Price CA,Puttonen E,
Reese JB,Rellán-Álvarez R,
Spalding EP,Sparks EE,Topp CN, Thegeometriesandtopologiesofleaves,flowers,roots,shoots,andtheirarrangements
Williams JHandChitwood DH(2017) have fascinated plant biologists and mathematicians alike. As such, plant morphology
MorphologicalPlantModeling:
is inherently mathematical in that it describes plant form and architecture with
UnleashingGeometric
andTopologicalPotentialwithin geometrical and topological techniques. Gaining an understanding of how to modify
thePlantSciences.
plant morphology, through molecular biology and breeding, aided by a mathematical
Front.PlantSci.8:900.
doi:10.3389/fpls.2017.00900 perspective, is critical to improving agriculture, and the monitoring of ecosystems
FrontiersinPlantScience|www.frontiersin.org 1 June2017|Volume8|Article900
fpls-08-00900 June8,2017 Time:16:13 #2
Buckschetal. PlantMorphologicalModeling
is vital to modeling a future with fewer natural resources. In this white paper, we begin
withanoverviewinquantifyingtheformofplantsandmathematicalmodelsofpatterning
in plants. We then explore the fundamental challenges that remain unanswered
concerningplantmorphology,fromthebarrierspreventingthepredictionofphenotype
from genotype to modeling the movement of leaves in air streams. We end with a
discussion concerning the education of plant morphology synthesizing biological and
mathematical approaches and ways to facilitate research advances through outreach,
cross-disciplinarytraining,andopenscience.Unleashingthepotentialofgeometricand
topological approaches in the plant sciences promises to transform our understanding
ofbothplantsandmathematics.
Keywords:plantbiology,plantscience,morphology,mathematics,topology,modeling
INTRODUCTION is an underlying repetitive process of transformation (Goethe,
1790; Friedman and Diggle, 2011). The modern challenge
Morphology from the Perspective of that Goethe’s paradigm presents is to quantitatively describe
Plant Biology transformations resulting from differences in the underlying
genetic, developmental, and environmental cues. From a
The study of plant morphology interfaces with all biological
mathematical perspective, the challenge is how to define shape
disciplines (Figure 1). Plant morphology can be descriptive
descriptors to compare plant morphology with topological
and categorical, as in systematics, which focuses on biological
and geometrical techniques and how to integrate these shape
homologiestodiscerngroupsoforganisms(Mayr,1981;Wiens,
descriptorsintosimulationsofplantdevelopment.
2000).Inplantecology,themorphologyofcommunitiesdefines
vegetationtypesandbiomes,includingtheirrelationshiptothe
MathematicstoDescribePlantShapeand
environment.Inturn,plantmorphologiesaremutuallyinformed
Morphology
byotherfieldsofstudy,suchasplantphysiology,thestudyofthe
Severalareasofmathematicscanbeusedtoextractquantitative
functionsofplants,plantgenetics,thedescriptionofinheritance,
measures of plant shape and morphology. One intuitive
andmolecularbiology,theunderlyinggeneregulation(Kaplan,
representation of the plant form relies on the use of skeletal
2001).
descriptors that reduce the branching morphology of plants to
Plant morphology is more than an attribute affecting plant
a set of intersecting lines or curve segments, constituting a
organization, it is also dynamic. Developmentally, morphology
mathematicalgraph.Theseskeleton-basedmathematicalgraphs
reveals itself over the lifetime of a plant through varying
can be derived from manual measurement (Godin et al.,
rates of cell division, cell expansion, and anisotropic growth
1999; Watanabe et al., 2005) or imaging data (Bucksch et al.,
(Esau, 1960; Steeves and Sussex, 1989; Niklas, 1994). Response
2010; Aiteanu and Klein, 2014). Such skeletal descriptions
to changes in environmental conditions further modulate
can be used to derive quantitative measurements of lengths,
the abovementioned parameters. Development is genetically
diameters,andanglesintreecrowns(BuckschandFleck,2011;
programmed and driven by biochemical processes that are
Raumonen et al., 2013; Seidel et al., 2015) and roots, at a
responsible for physical forces that change the observed
single time point (Fitter, 1987; Danjon et al., 1999; Lobet
patterning and growth of organs (Green, 1999; Peaucelle et al.,
et al., 2011; Galkovskyi et al., 2012) or over time to capture
2011; Braybrook and Jönsson, 2016). In addition, external
growth dynamics (Symonova et al., 2015). Having a skeletal
physicalforcesaffectplantdevelopment,suchasheterogeneous
descriptioninplaceallowsthedefinitionoforders,inabiological
soil densities altering root growth or flows of air, water, or
andmathematical sense,toenablemorphological analysisfrom
gravitymodulatingthebendingofbranchesandleaves(Moulia
a topological perspective (Figure 2A). Topological analyses
and Fournier, 2009). Inherited modifications of development
can be used to compare shape characteristics independently
over generations results in the evolution of plant morphology
of events that transform plant shape geometrically, providing
(Niklas, 1997). Development and evolution set the constraints
a framework by which plant morphology can be modeled.
forhowthemorphologyofaplantarises,regardlessofwhether
The relationships between orders, such as degree of self-
in a systematic, ecological, physiological, or genetic context
similarity (Prusinkiewicz, 2004) or self-nestedness (Godin and
(Figure1).
Ferraro, 2010) are used to quantitatively summarize patterns
of plant morphology. Persistent homology (Figure 2B), an
Plant Morphology from the Perspective
extension of Morse theory (Milnor, 1963), transforms a given
of Mathematics
plantshapegraduallytodefineself-similarity(MacPhersonand
In 1790, Johann Wolfgang von Goethe pioneered a perspective Schweinhart,2012)andmorphologicalproperties(Edelsbrunner
that transformed the way mathematicians think about plant and Harer, 2010; Li et al., 2017) on the basis of topological
morphology: the idea that the essence of plant morphology event statistics. In the example in Figure 2B, topological
FrontiersinPlantScience|www.frontiersin.org 2 June2017|Volume8|Article900
fpls-08-00900 June8,2017 Time:16:13 #3
Buckschetal. PlantMorphologicalModeling
FIGURE1|Plantmorphologyfromtheperspectiveofbiology.AdaptedfromKaplan(2001).Plantmorphologyinterfaceswithalldisciplinesofplantbiology—plant
physiology,plantgenetics,plantsystematics,andplantecology—influencedbybothdevelopmentalandevolutionaryforces.
events are represented by the geodesic distance at which Royer et al., 2009; Palacio-López et al., 2015; Chitwood et al.,
branches are “born” and “die” along the length of the 2016).
structure.
In the 1980s, David Kendall defined an elegant statistical MathematicstoSimulatePlantMorphology
framework to compare shapes (Kendall, 1984). His idea was Computersimulationsuseprinciplesfromgraphtheory,suchas
to compare the outline of shapes in a transformation-invariant graphrewriting,tomodelplantmorphologyoverdevelopmental
fashion. This concept infused rapidly as morphometrics into timebysuccessivelyaugmentingagraphwithverticesandedges
biology (Bookstein, 1997) and is increasingly carried out using asplantdevelopmentunfolds.Theserulesunravelthedifferences
machine vision techniques (Wilf et al., 2016). Kendall’s idea between observed plant morphologies across plant species
inspired the development of methods such as elliptical Fourier (Kurth,1994;Prusinkiewiczetal.,2001;BarthélémyandCaraglio,
descriptors(KuhlandGiardina,1982)andnewtrendsemploying 2007)andarecapableofmodelingfractaldescriptionsthatreflect
theLaplaceBeltramioperator(Reuteretal.,2009),bothrelying the repetitive and modular appearance of branching structures
on the spectral decompositions of shapes (Chitwood et al., (Horn, 1971; Hallé, 1971, 1986). Recent developments in
2012; Laga et al., 2014; Rellán-Álvarez et al., 2015). Beyond functional-structuralmodelingabstractthegeneticmechanisms
the organ level, such morphometric descriptors were used to driving the developmental program of tree crown morphology
analyzecellularexpansionratesofrapidlydeformingprimordia intoacomputationalframework(Runionsetal.,2007;Palubicki
into mature organ morphologies (Rolland-Lagan et al., 2003; et al., 2009; Palubicki, 2013). Similarly, functional-structural
Remmler and Rolland-Lagan, 2012; Das Gupta and Nath, modelingtechniquesareutilizedinrootbiologytosimulatethe
2015). efficiencyofnutrientandwateruptakefollowingdevelopmental
From a geometric perspective, developmental processes programs(Nielsenetal.,1994;Dunbabinetal.,2013).
construct surfaces in a three-dimensional space. Yet, the AlanTuring,apioneeringfigurein20th-centuryscience,hada
embedding of developing plant morphologies into a three- longstandinginterestinphyllotacticpatterns.Turing’sapproach
dimensional space imposes constraints on plant forms. totheproblemwastwofold:first,adetailedgeometricalanalysis
Awareness of such constraints has led to new interpretations of the patterns (Turing, 1992), and second, an application of
of plant morphology (Prusinkiewicz and de Reuille, 2010; histheoryofmorphogenesisthroughlocalactivationandlong-
Bucksch et al., 2014b) that might provide avenues to rangeinhibition(Turing,1952),whichdefinedthefirstreaction-
explain symmetry and asymmetry in plant organs (e.g., diffusion system for morphological modeling. Combining
Martinez et al., 2016) or the occurrence of plasticity as a physical experiments with computer simulations, Douady and
morphological response to environmental changes (e.g., Coudert(1996)subsequentlymodeledadiffusiblechemicalsignal
FrontiersinPlantScience|www.frontiersin.org 3 June2017|Volume8|Article900
fpls-08-00900 June8,2017 Time:16:13 #4
Buckschetal. PlantMorphologicalModeling
Hohmetal.,2010;Fujitaetal.,2011),thenumberoffloralorgans
(KitazawaandFujimoto,2015),theregularspacingofroothairs
(MeinhardtandGierer,1974),andtheestablishmentofspecific
vascularpatterns(Meinhardt,1976).
EMERGING QUESTIONS AND BARRIERS
IN THE MATHEMATICAL ANALYSIS OF
PLANT MORPHOLOGY
A true synthesis of plant morphology, which comprehensively
models observed biological phenomena and incorporates a
mathematical perspective, remains elusive. In this section, we
highlight current focuses in the study of plant morphology,
including the technical limits of acquiring morphological data,
phenotype prediction, responses of plants to the environment,
models across biological scales, and the integration of complex
phenomena, such as fluid dynamics, into plant morphological
models.
Technological Limits to Acquiring Plant
Morphological Data
There are several technological limits to acquiring plant
morphological data that must be overcome to move this field
forward. One such limitation is the acquisition of quantitative
plant images. Many acquisition systems do not provide
morphologicaldatawithmeasurableunits.Approachesthatrely
on the reflection of waves from the plant surface can provide
quantitativemeasurementsformorphologicalanalyses.Timeof
flightscanners,suchasterrestriallaserscanning,overcomeunit-
less measurement systems by recording the round-trip time of
hundreds of thousands of laser beams sent at different angles
fromthescannertothefirstplantsurfacewithinthelineofsight
(VosselmanandMaas,2010)(Figure3).Leveragingthespeedof
light allows calculation of the distance between a point on the
FIGURE2|Plantmorphologyfromtheperspectiveofmathematics.(A)The plantsurfaceandthelaserscanner.
topologicalcomplexityofplantsrequiresamathematicalframeworkto Laserscanningandthecomplementary,yetunitless,approach
describeandsimulateplantmorphology.Shownisthetopofamaizecrown
ofstereovisionbothproducesurfacesamplesorpointcloudsas
root42daysafterplanting.Colorrepresentsrootdiameter,revealingtopology
output. However, both approaches face algorithmic challenges
anddifferentordersofrootarchitecture.ImageprovidedbyJPL(Pennsylvania
StateUniversity).(B)Persistenthomologydeformsagivenplantmorphology encountered when plant parts occlude each other, since both
usingfunctionstodefineself-similarityinastructure.Inthisexample,a relyonthereflectionofwavesfromtheplantsurface(Bucksch,
geodesicdistancefunctionistraversedtothegroundlevelofatree(thatis, 2014). Radar provides another non-invasive technique to study
theshortestcurveddistanceofeachvoxeltothebaseofthetree),as
individual tree and forest structures over wide areas. Radar
visualizedinblueinsuccessiveimages.Thebranchingstructure,asdefined
pulses can either penetrate or reflect from foliage, depending
acrossscalesofthegeodesicdistancefunctionisrecordedasanH0
(zero-orderhomology)barcode,whichinpersistenthomologyrefersto on the selected wavelength (Kaasalainen et al., 2015). Most
connectedcomponents.Asthebranchingstructureistraversedbythe radarapplicationsoccurinforestryandarebeingoperatedfrom
function,connectedcomponentsare“born”and“die”asterminalbranches satellitesorairplanes.Althoughmorecompactandagilesystems
emergeandfusetogether.Eachofthesecomponentsisindicatedasabarin
are being developed for precision forestry above- and below-
theH0barcode,andthecorrespondenceofthebarcodetodifferentpointsin
thefunctionisindicatedbyverticallines,inpink.ImagesprovidedbyML ground(Fengetal.,2016),theirresolutionistoolowtoacquire
(DanforthPlantScienceCenter). thedetailinmorphologyneededtoapplyhierarchyorsimilarity
orientedmathematicalanalysisstrategies.
Imageacquisitionthatresolvesocclusionsbypenetratingplant
produced by a developing primordium that would inhibit the tissue is possible with X-ray (Kumi et al., 2015) and magnetic
initiationofnearbyprimordia,successfullyrecapitulatingknown resonance imaging (MRI; van Dusschoten et al., 2016). While
phyllotactic patterns in the shoot apical meristem (Bernasconi, both technologies resolve occlusions and can even penetrate
1994;Meinhardt,2004;Jönssonetal.,2005;Nikolaevetal.,2007; soil, their limitation is the requirement of a closed imaging
FrontiersinPlantScience|www.frontiersin.org 4 June2017|Volume8|Article900
fpls-08-00900 June8,2017 Time:16:13 #5
Buckschetal. PlantMorphologicalModeling
FIGURE3|TerrestriallaserscanningcreatesapointcloudreconstructionofaFinnishforest.(A)StructureofaborealforestsiteinFinlandasseenwithairborne
(ALS)andterrestrial(TLS)laserscanningpointclouds.Thered(ground)andgreen(above-ground)pointsareobtainedfromNationalLandSurveyofFinlandnational
ALSpointcloudsthatcoverhundredsofthousandsofsquarekilometerswithabout1pointpersquaremeterresolution.Theblueandmagentapointcloudsare
resultsoftwoindividualTLSmeasurementsandhaveover20millionpointseachwithinanareaofabout500m2.TLSpointdensityvarieswithrangebutcanbe
thousandsofpointspersquaremeteruptotensofmetersawayfromthescannerposition.(B)AnexcerptfromasingleTLSpointcloud(blue).TheTLSpointcloud
issodensethatindividualtreepointclouds(orange)andpartsfromthem(yellow)canbeselectedfordetailedanalysis.(C)AdetailfromasingleTLSpointcloud.
Individualbranches(yellow)20mabovegroundcanbeinspectedfromthepointcloudwithcentimeterlevelresolutiontoestimatetheirlengthandthickness.Images
providedbyEP(FinnishGeospatialResearchInstituteintheNationalLandSurveyofFinland).ALSdatawasobtainedfromtheNationalLandSurveyofFinland
TopographicDatabase,08/2012(NationalLandSurveyofFinlandopendatalicense,version1.0).
volume.Thus,althoughusefulforawidearrayofpurposes,MRI anatomycanbeimageddestructivelyusingconfocalmicroscopy
and X-ray are potentially destructive if applied to mature plant andlaserablation(Figure4)ornano-ormicro-CTtomography
organs such as roots in the field or tree crowns that are larger techniques,thatarelimitedtosmallpotvolumes,toinvestigate
than the imaging volume (Fiorani et al., 2012). Interior plant thefirstdaysofplantgrowth.
FrontiersinPlantScience|www.frontiersin.org 5 June2017|Volume8|Article900
fpls-08-00900 June8,2017 Time:16:13 #6
Buckschetal. PlantMorphologicalModeling
FIGURE4|Imagingtechniquestocaptureplantmorphology.(A)ConfocalsectionsofanArabidopsisroot.Theupperpanelshowsanewlateralrootprimordiumat
anearlystageofdevelopment(highlightedinyellow).Atregularintervalsnewrootsbranchfromtheprimaryroot.Thelowerpanelshowstheprimaryrootmeristem
andthestemcellniche(highlightedinyellow)fromwhichallcellsderive.Scalebars:100µm.ImagesprovidedbyAM(HeidelbergUniversity).(B)Computational
tomographic(CT)x-raysectionsthroughareconstructedmaizeear(leftandmiddle)andkernel(right).ImagesprovidedbyCT(DonaldDanforthPlantScience
Center).(C)Laserablationtomography(LAT)imageofanodalrootfromamature,field-grownmaizeplant,withcolorsegmentationshowingdefinitionofcortical
cells,aerenchymalacunae,andmetaxylemvessels.ImageprovidedbyJPL(PennsylvaniaStateUniversity).
FrontiersinPlantScience|www.frontiersin.org 6 June2017|Volume8|Article900
fpls-08-00900 June8,2017 Time:16:13 #7
Buckschetal. PlantMorphologicalModeling
The Genetic Basis of Plant Morphology geneticbasisofplasticity(Milleretal.,2007;Brooksetal.,2010;
Oneoftheoutstandingchallengesinplantbiologyistolinkthe SpaldingandMiller,2013).
inheritanceandactivityofgeneswithobservedphenotypes.This
is particularly challenging for the study of plant morphology, The Environmental Basis of Plant
as both the genetic landscape and morphospaces are complex: Morphology
modeling each of these phenomena alone is difficult, let alone Phenotypic plasticity is defined as the ability of one genotype
trying to model morphology as a result of genetic phenomena to produce different phenotypes based on environmental
(Benfey and Mitchell-Olds, 2008; Lynch and Brown, 2012; differences (Bradshaw, 1965; DeWitt and Scheiner, 2004) and
Chitwood and Topp, 2015). Although classic examples exist adds to the phenotypic complexity created by genetics and
in which plant morphology is radically altered by the effects development. Trait variation in response to the environment
of a few genes (Doebley, 2004; Clark et al., 2006; Kimura has been analyzed classically using ‘reaction norms,’ where the
et al., 2008), many morphological traits have a polygenic basis phenotypic value of a certain trait is plotted for two different
(Langlade et al., 2005; Tian et al., 2011; Chitwood et al., environments (Woltereck, 1909). If the trait is not plastic, the
2013). slopeofthelineconnectingthepointswillbezero;ifthereaction
Quantitative trait locus (QTL) analyses can identify the norm varies across the environment the trait is plastic and the
polygenic basis for morphological traits that span scales from slopeofthereactionnormlinewillbeameasureoftheplasticity.
the cellular to the whole organ level. At the cellular level, root Asmostoftheresponsesofplantstotheirenvironmentarenon-
cortexcellnumber(Ronetal.,2013),thecellularbasisofcarpel linear, more insight into phenotypic plasticity can be obtained
size (Frary et al., 2000), and epidermal cell area and number by analyzing dose-response curves or dose-response surfaces
(Tisné et al., 2008) have been analyzed. The genetic basis of (Mitscherlich,1909;Poorteretal.,2010).
cellular morphology ultimately affects organ morphology, and Seminal work by Clausen et al. (1941) demonstrated using
quantitative genetic bases for fruit shape (Paran and van der several clonal species in a series of reciprocal transplants that,
Knaap,2007;Monforteetal.,2014),rootmorphology(Zhuetal., although heredity exerts the most measureable effects on plant
2005; Clark et al., 2011; Topp et al., 2013; Zurek et al., 2015), morphology, environment is also a major source of phenotypic
shootapicalmeristemshape(Leiboffetal.,2015;Thompsonetal., variability.Researchcontinuestoexploretherangeofphenotypic
2015),leafshape(Langladeetal.,2005;Kuetal.,2010;Tianetal., variationexpressedbyagivengenotypeinthecontextofdifferent
2011;Chitwoodetal.,2014a,b;Zhangetal.,2014;Truongetal., environments,whichhasimportantimplicationsformanyfields,
2015), and tree branching (Kenis and Keulemans, 2007; Segura includingconservation,evolution,andagriculture(Nicotraetal.,
2010; DeWitt, 2016). Many studies examine phenotypes across
etal.,2009)havebeendescribed.
latitudinaloraltitudinalgradients,orotherenvironmentalclines,
Natural variation in cell, tissue, or organ morphology
tocharacterizetherangeofpossiblevariationanditsrelationship
ultimatelyimpactsplantphysiology,andviceversa.Forexample,
totheprocessoflocaladaptation(Cordelletal.,1998;Díazetal.,
formationofrootcorticalaerenchymawaslinkedtobetterplant
2016).
growthunderconditionsofsuboptimalavailabilityofwaterand
Below-ground, plants encounter diverse sources of
nutrients (Zhu et al., 2010; Postma and Lynch, 2011; Lynch,
environmental variability, including water availability, soil
2013),possiblybecauseaerenchymareducesthemetaboliccosts
chemistry, and physical properties like soil hardness and
of soil exploration. Maize genotypes with greater root cortical
movement.Thesefactorsvarybetweenindividualplants(Razak
cell size or reduced root cortical cell file number reach greater
etal.,2013)andwithinanindividualrootsystem,whereplants
depths to increase water capture under drought conditions,
respond at spatio-temporal levels to very different granularity
possibly because those cellular traits reduce metabolic costs of
(Drew,1975;RobbinsandDinneny,2015).Plasticityatamicro-
root growth and maintenance (Chimungu et al., 2015). The
environmental scale has been linked to developmental and
control of root angle that results in greater water capture in
molecularmechanisms(Baoetal.,2014).Thescientificchallenge
rice as water tables recede was linked to the control of auxin
hereistointegratetheseeffectsatawholerootsystemleveland
distribution (Uga et al., 2013). Similarly, in shoots, natural
use different scales of information to understand the optimal
variationcanbeexploitedtofindgeneticlocithatcontrolshoot
acquisitioninresourcelimitedconditions(Rellán-Álvarezetal.,
morphology, e.g., leaf erectness (Ku et al., 2010; Feng et al.,
2016)(Figure5).
2011).
High-throughput phenotyping techniques are increasingly
Integrating Models from Different Levels
used to reveal the genetic basis of natural variation (Tester
and Langridge, 2010). In doing so, phenotyping techniques of Organization
complementclassicapproachesofreversegeneticsandoftenlead Sinceitisextremelydifficulttoexaminecomplexinterdependent
tonovelinsights,eveninawell-studiedspecieslikeArabidopsis processes occurring at multiple spatio-temporal scales,
thaliana. Phenotyping techniques have revealed a genetic basis mathematical modeling can be used as a complementary
for dynamic processes such as root growth (Slovak et al., 2014) tool with which to disentangle component processes and
and traits that determine plant height (Yang et al., 2014). investigate how their coupling may lead to emergent patterns
Similarly, high-resolution sampling of root gravitropism has at a systems level (Hamant et al., 2008; Band and King, 2012;
led to an unprecedented understanding of the dynamics of the Band et al., 2012; Jensen and Fozard, 2015). To be practical, a
FrontiersinPlantScience|www.frontiersin.org 7 June2017|Volume8|Article900
fpls-08-00900 June8,2017 Time:16:13 #8
Buckschetal. PlantMorphologicalModeling
FIGURE5|Theenvironmentalbasisofplantmorphology.RootsystemarchitectureofArabidopsisCol-0plantsexpressingProUBQ10:LUC2ogrowingin(A)control
and(B)water-deficientconditionsusingtheGLO-Rootssystem(Rellán-Álvarezetal.,2015).ImagesprovidedbyRR-Á(LaboratorioNacionaldeGenómicaparala
Biodiversidad,CINVESTAV)areacompositeofavideooriginallypublished(Rellán-Álvarezetal.,2015).
multiscale model should generate well-constrained predictions cell growth and division with the spatio-temporal dynamics of
despite significant parameter uncertainty (Gutenkunst et al., theproteinsinvolvedinstemcellregulationandsimulatesshoot
2007;Hofhuisetal.,2016).Itisdesirablethatamultiscalemodel apical meristem development in wild type and mutant plants
hascertainmodularityinitsdesignsuchthatindividualmodules (Figure6B).
areresponsibleformodelingspecificspatialaspectsofthesystem
(Baldazzietal.,2012).Imagingtechniquescanvalidatemultiscale
Modeling the Impact of Morphology on
models(e.g.,Willisetal.,2016)suchthatsimulationscanreliably
guideexperimentalstudies. Plant Function
To illustrate the challenges of multi-scale modeling, Quantitative measures of plant morphology are critical to
we highlight an example that encompasses molecular and understand function. Vogel (1989) was the first to provide
cellular scales. At the molecular scale, models can treat some quantitativedatathatshowedhowshapechangesinleavesreduce
biomoleculesasdiffusive,butothers,suchasmembrane-bound drag or friction in air or water flows. He found that single
receptors, can be spatially restricted (Battogtokh and Tyson, broadleavesreconfigureathighflowvelocitiesintoconeshapes
2016). Separately, at the cellular scale, mathematical models to reduce flutter and drag (Figures 7A,B). More recent work
describe dynamics of cell networks where the mechanical discovered that the cone shape is significantly more stable than
pressuresexertedonthecellwallsareimportantfactorsforcell other reconfigurations such as U-shapes (Miller et al., 2012).
growth and division (Jensen and Fozard, 2015) (Figure 6A). Subsequent experimental studies on broad leaves, compound
In models describing plant development in a two-dimensional leaves,andflowersalsosupportrapidrepositioninginresponse
cross-section geometry, cells are often modeled as polygons to strong currents as a general mechanism to reduce drag
definedbywallsbetweenneighboringcells.Thespatialposition (Niklas,1992;Ennos,1997;EtnierandVogel,2000;Vogel,2006)
of a vertex, where the cell walls of three neighboring cells (Figure 7C). It is a combination of morphology and anatomy,
coalesce,isaconvenientvariableformathematicalmodelingof andtheresultantmaterialproperties,whichleadtotheseoptimal
the dynamics of cellular networks (Prusinkiewicz and Runions, geometricre-configurationsofshape.
2012).Amultiscalemodelcanthenbeassembledbycombining From a functional perspective, it is highly plausible that leaf
themolecularandcellularmodels.Mutationsanddeletionsofthe shapeandsurface-materialpropertiesaltertheboundarylayerof
genes encoding the biomolecules can be modeled by changing afluid/gasovertheleafsurfaceorenhancepassivemovementthat
parameters. By inspecting the effects of such modifications canpotentiallyaugmentgasandheatexchange.Forexample,it
on the dynamics of the cellular networks, the relationship hasbeenproposedthatthebroadleavesofsometreesflutterfor
between genotypes and phenotypes can be predicted. For thepurposeofconvectiveandevaporativeheattransfer(Thom,
example, Fujita et al. (2011) model integrates the dynamics of 1968; Grant, 1983). Any movement of the leaf relative to the
FrontiersinPlantScience|www.frontiersin.org 8 June2017|Volume8|Article900
fpls-08-00900 June8,2017 Time:16:13 #9
Buckschetal. PlantMorphologicalModeling
FIGURE6|Integrationoftissuegrowthandreaction-diffusionmodels.(A)Vertexmodelofcellularlayers(PrusinkiewiczandLindenmayer,1990).K,(cid:69)la,and(cid:69)l0are
thespringconstant,currentlength,andrestlengthforwalla.KPisaconstantandSAisthesizeofcellA.(cid:49)tistimestep.Shownisasimulationofcellnetwork
growth.(B)ReactiondiffusionmodeloftheshootapicalmeristemforWUSCHELandCLAVATAinteractions(Fujitaetal.,2011).u=WUS,v=CLV,i=cellindex,(cid:56)is
asigmoidfunction.E,B,AS,Ad,C,D,um,Du,Dvarepositiveconstants.ShownarethedistributionsofWUSandCLVlevelswithinadynamiccellnetwork.Images
providedbyDB(VirginiaTech).
movement of the air or water may decrease the boundary layer Education
and increase gas exchange, evaporation, and heat dissipation Mathematics has been likened to “biology’s next microscope,”
(Roden and Pearcy, 1993). Each of these parameters may be because of the insights into an otherwise invisible world
altered by the plant to improve the overall function of the leaf it has to offer. Conversely, biology has been described as
(Vogel,2012). “mathematics’ next physics,” stimulating novel mathematical
Thegrowthoftheplantcontinuouslymodifiesplanttopology approaches because of the hitherto unrealized phenomena that
and geometry, which in turn changes the balance between biologystudies(Cohen,2004).Thescaleoftheneededinterplay
organ demand and production. At the organismal scale, the between mathematics and plant biology is enormous and may
3D spatial distribution of plant organs is the main interface lead to new science disciplines at the interface of both: ranging
between the plant and its environment. For example, the 3D from the cellular, tissue, organismal, and community levels to
arrangementofbranchesimpactslightinterceptionandprovides the global; touching upon genetic, transcriptional, proteomic,
the support for different forms of fluxes (water, sugars) and metabolite, and morphological data; studying the dynamic
signals (mechanical constraints, hormones) that control plant interactions of plants with the environment or the evolution
functioningandgrowth(GodinandSinoquet,2005). of new forms over geologic time; and spanning quantification,
statistics,andmechanisticmathematicalmodels.
Research is becoming increasingly interdisciplinary, and
MILESTONES IN EDUCATION AND undergraduate, graduate, and post-graduate groups are actively
OUTREACH TO ACCELERATE THE trying to bridge the gap between mathematics and biology
skillsets. While many graduate programs have specialization
INFUSION OF MATH INTO THE PLANT
tracks under the umbrella of mathematics or biology-specific
SCIENCES
programs, increasingly departments are forming specially
designed graduate groups for mathematical/quantitative
Mathematicsandplantbiologyneedtointeractmorecloselyto ,
biology1 2 to strengthen the interface between both disciplines.
accelerate scientific progress. Opportunities to interact possibly
involve cross-disciplinary training, workshops, meetings, and
1BioQuant at University of Heidelberg, http://www.bioquant.uni-heidelberg.de
funding opportunities. In this section, we outline perspectives
(retrievedFebruary28,2017)
for enhancing the crossover between mathematics and plant 2Quantitative Biosciences at Georgia Tech in Atlanta, http://qbios.gatech.edu
biology. (retrievedFebruary28,2017)
FrontiersinPlantScience|www.frontiersin.org 9 June2017|Volume8|Article900